Question

Problem 1. Let D be the region bounded by the parabola y = x and the line y = 8. Find Could you guess the answer to part a) without a computation? How?

Answer 1

Problem: 3 22 2 The point of intersection of y=% and 928 will be find by putting y 28 in Y=n² x = 4282 a) ada Here is the region bounded by y = x² and y=8. & x² - Race ada y from above dAz dx dy where value of avorry from 252 to 252 valie of & vorry from ² to 8 2128 I 25 xdxdx I a 2 de (x) dx

Se pare (8x - 2) de 5:46.87cont]-[629.com 5- [4.27. 09*7-(4.28.)".com *) och

o & dA here also the D-region bounded by & x² and line x=8. so, dAz dady where & varies from –252 to 252. and & varies from x² to 8. 212 8 Ingre de de -2/2 22 I 2 (2 2 ² (8 - x²) dx 12 Iz (8 x3 = x)dx 252

STUD PAGE NO DATE Iz so $ (er) – 65)$ 220140 12 16 (2) - 2 cari) Iz 14 I= 48.28

also in a sada as we put the value of dA z dedy we get, 352 Iz ( x (8 - x²) dx that a(8 - x²) is from above we see a odd function. and for odd function f(x) dx = so, by knowing that a(8-n²) is odd. function we can directly write the value of integral as zero,